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# Matt gets a \$1,000 commission on a big sale. This commission alone

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Math Expert
Joined: 02 Sep 2009
Posts: 52296
Matt gets a \$1,000 commission on a big sale. This commission alone  [#permalink]

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30 Jun 2015, 04:02
1
9
00:00

Difficulty:

65% (hard)

Question Stats:

62% (01:56) correct 38% (02:05) wrong based on 184 sessions

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Matt gets a \$1,000 commission on a big sale. This commission alone raises his average commission by \$150. If Matt's new average commission is \$400, how many sales has Matt made?

A. 3
B. 4
C. 5
D. 6
E. 7

Kudos for a correct solution.

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Joined: 26 Dec 2011
Posts: 114
Schools: HBS '18, IIMA
Re: Matt gets a \$1,000 commission on a big sale. This commission alone  [#permalink]

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30 Jun 2015, 05:45
Matt gets a \$1,000 commission on a big sale. This commission alone raises his average commission by \$150. If Matt's new average commission is \$400, how many sales has Matt made?

A. 3
B. 4
C. 5
D. 6
E. 7

Solution -

For \$1000 commission, average commission increased \$150.
Old Commission = 400 - 150 = 250
For \$X commission, average commission was \$250.

(1000/X) = 150/250 = 3/5 -----------> For \$1000 commission, Matt made a sales of 3. ANS A.
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Thanks,

Math Expert
Joined: 02 Aug 2009
Posts: 7209
Matt gets a \$1,000 commission on a big sale. This commission alone  [#permalink]

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30 Jun 2015, 05:52
1
2
balamoon wrote:
Matt gets a \$1,000 commission on a big sale. This commission alone raises his average commission by \$150. If Matt's new average commission is \$400, how many sales has Matt made?

A. 3
B. 4
C. 5
D. 6
E. 7

Solution -

For \$1000 commission, average commission increased \$150.
Old Commission = 400 - 150 = 250
For \$X commission, average commission was \$250.

(1000/X) = 150/250 = 3/5 -----------> For \$1000 commission, Matt made a sales of 3. ANS A.

Hi,
i think you are wrong..
initial average =400-150=250...
let the sales be n, so total commission=250n...
now we are increasing the sale by one and commission becomes 400....
so total commission=(n+1)*400....
this should be equal to 250n+1000 (1000 is the amount of new commission on n+1 th sale..)
(n+1)*400=250n+1000..
150n=600..
n=4..
total sales =4+1=5..
ans C
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Posts: 108
Re: Matt gets a \$1,000 commission on a big sale. This commission alone  [#permalink]

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30 Jun 2015, 06:03
1
Bunuel wrote:
Matt gets a \$1,000 commission on a big sale. This commission alone raises his average commission by \$150. If Matt's new average commission is \$400, how many sales has Matt made?

A. 3
B. 4
C. 5
D. 6
E. 7

Kudos for a correct solution.

New Average Commission = \$400, which increased by \$150 => Old Aver commission = 400 - 150 = 250

1000 + 250X = 400 [x + 1] => X = 4 => x+1=5
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Re: Matt gets a \$1,000 commission on a big sale. This commission alone  [#permalink]

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30 Jun 2015, 06:07
1
Bunuel wrote:
Matt gets a \$1,000 commission on a big sale. This commission alone raises his average commission by \$150. If Matt's new average commission is \$400, how many sales has Matt made?

A. 3
B. 4
C. 5
D. 6
E. 7

Kudos for a correct solution.

Let, Average Commission = x
No. of items sold = y
Total Commission = xy

New Commission = xy+1000
New Average = (xy+1000) / (y+1) = 150+x
i.e. (xy+1000) = (y+1)* (150+x)
i.e. (xy+1000) = (xy+x+150y+150)
i.e. (850) = (x+150y)

New Commission = 400 = 150+x
i.e. x=250
i.e. y = 4

New Sales = y+1 = 5

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Joined: 20 Jul 2011
Posts: 80
GMAT 1: 660 Q49 V31
Re: Matt gets a \$1,000 commission on a big sale. This commission alone  [#permalink]

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30 Jun 2015, 08:52
1
Bunuel wrote:
Matt gets a \$1,000 commission on a big sale. This commission alone raises his average commission by \$150. If Matt's new average commission is \$400, how many sales has Matt made?

A. 3
B. 4
C. 5
D. 6
E. 7

Kudos for a correct solution.

This is like a weighted average problem.
Assume, the no of sales made by Matt as x
Adding Rs. 1000 for a new sale, increases his average commission to Rs. 400

hence,
Avg. Commission = (250x + 1000) / (x + 1) = 400
Solving for x, x = 600 / 150, x = 4.

But, No of sale made by Matt including the big sale = x + 1 => 4+1 => 5

Options C
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Matt gets a \$1,000 commission on a big sale. This commission alone  [#permalink]

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Updated on: 30 Jun 2015, 10:16
1
# of sale =n; new avg = 400 -150 =250
hence final equation will be 1000+250n= 400(n+1); solving for n, we get n=4
total sale=5

Thanks,

Originally posted by lipsi18 on 30 Jun 2015, 09:31.
Last edited by lipsi18 on 30 Jun 2015, 10:16, edited 1 time in total.
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Re: Matt gets a \$1,000 commission on a big sale. This commission alone  [#permalink]

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30 Jun 2015, 09:58
2
suppose no. of commisions made before latest commision = n

old average commision = 400 - 150 =250

Now ,

(n*250 + 1000 )/ n+1 = 400
so , 250n+1000 = 400n +400

150n = 600
n = 4

we need to add latest commision , so answer = 4+1 = 5

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Joined: 07 Apr 2015
Posts: 164
Re: Matt gets a \$1,000 commission on a big sale. This commission alone  [#permalink]

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01 Jul 2015, 06:59
1
Old average commission:

S/n = 250
S = 250*n

New average commission:
(S + 1000) / (n + 1) = 400 Insert S

(250n + 1000) = (400n + 400)
600 = 150n
n = 4

n+1 = 5
Math Expert
Joined: 02 Sep 2009
Posts: 52296
Re: Matt gets a \$1,000 commission on a big sale. This commission alone  [#permalink]

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06 Jul 2015, 02:13
Bunuel wrote:
Matt gets a \$1,000 commission on a big sale. This commission alone raises his average commission by \$150. If Matt's new average commission is \$400, how many sales has Matt made?

A. 3
B. 4
C. 5
D. 6
E. 7

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

Before the \$1,000 commission, Matts average commission was \$250; you can express this algebraically with the equation S = 250n.

After the sale, the sum of Matts sales increased by \$1,000, the number of sales made increased by 1, and his average commission was \$400. You can express this algebraically with the equation:

S + 1,000 = 400(n + 1)

250n + 1,000 = 400(n + 1)
250n + 1,000 = 400n + 400
150n = 600
n = 4

Before the big sale, Matt had made 4 sales. Including the big sale, Matt has made 5 sales.

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Posts: 9454
Re: Matt gets a \$1,000 commission on a big sale. This commission alone  [#permalink]

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18 Apr 2018, 22:06
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Re: Matt gets a \$1,000 commission on a big sale. This commission alone &nbs [#permalink] 18 Apr 2018, 22:06
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